Solve for $x$ and $y$ using elimination. ${-6x+y = -42}$ ${-5x-y = -46}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-11x = -88$ $\dfrac{-11x}{{-11}} = \dfrac{-88}{{-11}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-6x+y = -42}\thinspace$ to find $y$ ${-6}{(8)}{ + y = -42}$ $-48+y = -42$ $-48{+48} + y = -42{+48}$ ${y = 6}$ You can also plug ${x = 8}$ into $\thinspace {-5x-y = -46}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ - y = -46}$ ${y = 6}$